I'm no UBI expert, but I don't think you understand the point of UBI: universal basic income. I would argue (again no expert here) it's more about constant economic injection, providing a baseline to reduce risk of entrepreneurship and generally providing a higher quality of life to the 99%'ers.
As far as paying for it or finding the right way to make it happen in the US, I agree that there are a ton of roadblocks. Right now welfare is at $1.3 trillion, let's say that was increased to $2 trillion; divide by 300 million Americans and you've got over $6,500 per American per year. Just over half of what you stated is the typical amount discussed. That being said, I could certainly find a good use for an extra $500+ a month in income.
> How exactly do you convince a nation which already isn't willing to pay for healthcare to pay for basic income, too?
I think it's the politicians and the news media that twists this, Americans in polls generally do support single-payer health care and I would posit this same sentiment would be shared for basic income (if not more support since it's quite a bit easier to understand)